The structure of fibers of deoxyhemoglobin S has been under investigation for several years and a number of different models have been proposed for the arrangement of molecules within the particles. We have used reconstruction and modeling techniques in our analysis of these structures. Several new approaches have been employed in this analysis in order to provide improved estimates of the co-ordinates, pairing, and polarity of the hemoglobin S molecules. Fibers have a variable pitch and, in order to minimize distortions in the reconstructed density maps associated with these variations in pitch, we have developed an iterative procedure to measure the instantaneous pitch and have modified the reconstruction algorithm to incorporate the measured values. This procedure improves the accuracy with which the hemoglobin S molecules can be located in the density maps. Furthermore, the determination of the instantaneous pitch allows us to measure directly the rotation of the individual hemoglobin molecules. These measurements are in excellent agreement with the values predicted using a random angular walk model (as originally proposed for F-actin) to describe the variable pitch. The reconstructions confirm that the fiber consists of 14 strands of hemoglobin S arranged in a hexagonally shaped cross-section. We have determined the pairing of the molecules to form double strands directly from the density maps by identifying the molecules that have intermolecular distances that conform to those of double strands in the Wishner-Love crystal. The seven double strands identified in this manner are consistent with the strand pairings proposed by Dykes et al. (1979) rather than the alternate pairings proposed by Rosen & Magdoff-Fairchild (1985). In addition, we have for the first time determined the polarity of the double strands directly from the reconstruction data. This was achieved using a procedure that amounts to essentially "dissecting" individual double strands from the reconstructed density maps so that their density distribution could be examined independently of the neighboring double strands. Knowledge of the relative polarities of the double strands is essential for determining the intermolecular interactions that stabilize the fiber.